Over the past year, the majority of my research on this project was performed in two areas: (1) censored failure-time analysis when some censoring indicators are missing and (2) analysis of historical control data in rodent carcinogenicity experiments. These two areas of research are described in more detail below. I also revised an entry in the Encyclopedia of Environmetrics about the general problem of using a 3-state stochastic model to analyze data from animal carcinogenicity studies. Area 1: Failure-time data are typically subject to censoring, such as when a study ends before all participants fail. Additionally, when multiple causes of failure are operating, the time to failure from one cause can be censored by a failure from another cause. In some situations, the censoring indicator is missing for a subset of individuals, such as in a cancer bioassay when the pathologist is not able to determine the role of a tumor in causing death or when some records are incomplete. The analysis of failure-time data typically focuses on hazard functions. Under an accelerated failure-time model, we derived three nonparametric hazard estimators that are appropriate when some failure times are right censored and some censoring indicators are missing. Specifically, we developed a regression surrogate estimator, an imputation estimator, and an inverse probability weighted estimator. All three estimators use kernel smoothing techniques and enjoy certain large-sample properties such as uniform strong consistency and asymptotic normality. A simulation study showed that the proposed hazard estimators also performed well in small samples. Under the same accelerated failure-time model, we also developed a regression analysis, which allows us to evaluate the effects of various explanatory variables on the hazard functions. We wrote two articles describing our work in this general area. For the homogeneous estimation problem, our first paper is in press at the Annals of the Institute of Statistical Mathematics. For the regression analysis, our second paper was published in Lifetime Data Analysis. I also gave an invited talk about this research at the International Chinese Statistical Association Applied Statistics Symposium in New York City on June 27, 2011. Area 2: When evaluating the carcinogenicity of a chemical, researchers often assess tumor incidence rates from the current rodent bioassay within the context of a historical database of control tumor rates from similar studies using animals of the same species, strain, and sex. If the tumor rate in the control group of the current study is outside the range of historical control rates, there may be concern about the validity of the conclusions drawn from the current study. When comparing tumor rates in current and historical control groups, our research demonstrated that a decision rule based on the historical range does not maintain the Type I error rate at the usual 5% signi&#64257;cance level and can, in fact, be as high as 67% in some real-world situations. In other cases, the power can go to zero. We developed a simple alternative procedure that controls Type I errors, adjusts for animal survival, and accounts for extra variability between studies. Extensive simulations showed that our test operated at or below the nominal level, whereas the range-based decision rule often resulted in extremely high Type I error rates. In other research related to historical control data, we compared tumor incidence rates in two strains of rats used in NTP studies. Specifically, in 2008 the NTP switched from using Fischer 344/N (F344/N) rats to using Harlan Sprague Dawley (SD) rats in its carcinogenicity, reproductive and immunotoxicity bioassays. The NTP had previously used female SD rats in nine chronic bioassays. We compared historical control tumor data from these nine SD studies with historical control tumor data from matched NTP chronic bioassays that used F344/N rats. Our goal was to identify similarities and differences in tumor incidence rates across the two strains. Matching on sex, diet, route, and laboratory led to nine comparable F344/N studies. All tumor types with fewer than 3 occurrences in the entire historical control database were excluded, as were metastases and combinations of tumors, leaving a total of 82 tumor types. Statistically significant strain differences in incidence rates were identified for several tumor types, including clitoral gland adenoma, mammary gland fibroadenoma, mammary gland carcinoma, thyroid gland C-Cell adenoma, and mononuclear cell leukemia. When vehicle was included as an additional matching criterion, the number of comparable F344/N studies dropped to four, but similar results were obtained. Our paper about the comparison of current and historical control tumor rates was published in Statistics in Biopharmaceutical Research and our paper regarding the comparison of control tumor rates in SD and F344/N rats was published in Toxicologic Pathology. This research was conducted in collaboration with Dr. Shyamal Peddada and is also mentioned in the report for his project entitled 'Statistical Methods with Applications to Toxicology and Microarray Data'(ES101744).